Patrick had 2,000 ducks and chickens on his farm. He had 3 times as many chickens as ducks. After selling some chickens, he now has twice as many ducks as chickens. How many chickens did he sell?
+313 Let Patrick had 'x' number of Ducks.
Since he had 3 times as many chickens as ducks.
∴ Number of chickens Patrick had = 3x
Since he had a total of 2000 Ducks and chickens,
∴ 3x + x = 2000
⇒ 4x = 2000
⇒ x = 500
∴ Number of Ducks Patrick had = 500
And number of Chickens Patrick had = 3x = 3 × 500 = 1500
Now he sells some chicken and after selling he now has twice as many ducks as chickens.
Let he sells 'y' number of chickens,
∴ Number of chickens left = 1500 - y
And the number of Ducks = 500
he now has twice as many ducks as chickens.
∴ 2 × (1500 - y) = 500
⇒ 3000 - 2y = 500
⇒ 2y = 2500
⇒ y = 1250
this means that he sold 1250 chickens.
ANSWER :
Number of chickens Patrick sold = 1250
